Differential
Inclusions, Control and Optimization 20 (2000) 195-207

doi: 10.7151/dmdico.1012

Marcin Studniarski

*Faculty of Mathematics, University of Łódź
ul. S. Banacha 22, 90-238 Łódź, Poland*

We present a characterization of weak sharp local minimizers of order one for a
function f:R^{n}∪ R defined by f(x): = max{f_{i}(x)|i =
1,...,p}, where the functions f_{i} are strictly differentiable. It is given in
terms of the gradients of f_{i} and the Mordukhovich normal cone to a given set on
which f is constant. Then we apply this result to a smooth nonlinear programming problem
with constraints.

**Keywords and phrases:** weak sharp minimizer of order one, maximum function,
strictly differentiable function, normal cone.

**1991 Mathematics Subject Classification:** 49J52; 49K35.

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Received 10 December 1999

Revised 7 May 2000